DELIVERABLE 3.3.4

FP7-ENERGY-2008-TREN-1

Grant Agreement No: 239349

ACRONYM: H2-IGCC

Preliminary Turbine Cooling Requirement

Mechanical and Industrial Engineering Department

RO3 Scientific Responsible: Prof. Giovanni Cerri

Collaborators:

F. Botta, L. Chennaoui, A. Giovannelli, C. Salvini, C. Basilicata, S. Mazzoni, E. Archilei

DISSEMINATION LEVEL: PUBLIC Date of issue 01-08-2013

Deliverable 3.3.4

Preliminary Turbine Cooling Requirement

Please send your feedback to G. Cerri, Organisation: RO3, cerri@uniroma3.it

DISSEMINATION LEVEL: PUBLIC

Page 3 of 45

Index

Index ........................................................................................................................................... 3

Index of figures .......................................................................................................................... 4

Nomenclature ............................................................................................................................. 6

1 Introduction ......................................................................................................................... 8

2 Uncooled Cycle Calculation .............................................................................................. 10

3 GT Global Model for the evaluation of the overall cooling mass flow ............................ 14

4 Heat transfer scheme and cooling scheme ........................................................................ 17

4.1 Flow in the Expander Stages ...................................................................................... 19

5 Lumped Performance Features Model .............................................................................. 25

6 Blade Cooling Model ........................................................................................................ 26

6.1 Cooling Effectiveness ................................................................................................ 32

6.1.2 Effectiveness – Number of heat Transfer Unit .................................................... 32

7 Design Point Result ........................................................................................................... 39

8 Off – Design ...................................................................................................................... 41

Reference .................................................................................................................................. 44

Page 4 of 45

Index of figures

Fig. 1: Scheme of a GT Brayton Cycle – Not to Scale ............................................................ 10

Fig. 2: Scheme of a Generic 300MW F Class GT ................................................................... 10

Table 1: HD GTs Characteristic Quantities ............................................................................. 11

Table 2: Input Data for Cycle Calculation ............................................................................... 12

Table 3: Cycle Calculated Quantities ....................................................................................... 12

Table 4: Cycle Mass Flows ...................................................................................................... 13

Fig. 3: Turbine Inlet Temperature Nomenclature .................................................................... 13

Table 5: Evaluation of the overall coolant mass flow .............................................................. 14

for various coolant and blade temperature, respectively .......................................................... 14

Fig. 4: Sketch of the GT presented in the paper [13] ............................................................... 15

Fig. 5: Cross Section of the Cooling Paths (SIEMENS) .......................................................... 17

Fig. 6: Schematic View of the main stream and coolant streams along the combustor ........... 18

and of the heat fluxes moving through the GT to the casing and to the inner components

(shaft, disk, etc.) ....................................................................................................................... 18

Fig. 7: Schematic view of the cooling paths along the disks – As example ............................ 19

Fig. 8: Example of a Generic Gas Turbine Cooling Path along Stator and Rotor Row ........... 20

Fig. 9: Schematic View of the Cooled components of the Stator Row – As Example ............ 21

Fig. 10: Typical Temperature Distribution along a 1st Stage Aeronautic Rotor Disk – As

Example .................................................................................................................................... 21

Fig. 11: Schematic View of a 1st Nozzle Vane Cooling Components – As Example .............. 22

Fig. 12: Schematic View of a 1st Rotor Blade Cooling Components – As Example .............. 22

Fig. 13: Comparison between cooled blade and uncooled blade coolant flow ........................ 23

Table 6: Fractions of the overall mass flow for each row (in percentage %) .......................... 23

Fig. 14: Schematic View of the cooling path ........................................................................... 24

from the compressor bleeding station to the expander row injection station ........................... 24

Fig. 15 a-b: sketch of the lumped approach for heat transfer devices ...................................... 25

Fig. 16: Sketch of a Rotor Blade temperature distribution along the layers ............................ 26

Fig. 17: Simplified view of the thermal resistance for a generic blade .................................... 27

Fig 18: Schematic view of the enhance system of the internal heat transfer coefficient ......... 28

Fig. 19 a-b: a) rib distribution – b) Influence of Turbulent promoter on the NU number ....... 28

Fig 20 : Influence of jet impingement architecture on internal heat transfer coefficient ......... 29

Fig 21: Schematic view of the depression of the external heat transfer coefficient owing to the

film cooling .............................................................................................................................. 30

Fig. 22: Typical heat transfer distribution among the blade row surface ................................. 30

Fig. 23: External heat transfer coefficient depressed by the film cooling ................................ 31

Fig. 24: Influence of the Thickness TBC layer on the coolant flows ....................................... 31

Fig. 25: Temperature profile along the various blade layers .................................................... 32

Fig. 26: schematically main stream temperature decrease – Not to scale ................................ 34

Fig. 27: RO3 Cooling Design Curve – Stator Row and Rotor Row ........................................ 36

Fig. 28: Cooling Effectiveness versus Thermal Capacity Ratio .............................................. 37

Fig. 29: SoA – Gross Cooling Effectiveness VS Heat Loading Parameter ............................. 38

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Fig. 30: SoA –Cooling Effectiveness VS Coolant/Gas Heat capacity flux ratio ..................... 38

Fig. 31: SoA –Cooling Effectiveness VS TCR ........................................................................ 38

Fig. 32: 1st Nozzle Vane re-staggering – As Example ............................................................. 39

Table 7: Sizing Data – Methane ............................................................................................... 39

Table 8: Results of the Lumped Model for cooling requirement (Methane) ........................... 40

Table 9: Sizing Data – 33MJ/kg Syngas .................................................................................. 40

Table 10: Results of the Lumped Model for cooling requirement (33MJ/kg Syngas) ............ 40

Fig. 33: Comparison between RO3 and Kim-Ro off design model ......................................... 41

Fig. 34: Uncooled Blade Row Scheme – As Example ............................................................. 42

Fig. 35: Off-Design cooling effectiveness VS TCR ................................................................ 43

Page 6 of 45

Nomenclature

BAT Best Available Technology

BM Bulk Material

cp specific heat capacity

CC Combustion Chamber

CFD Computational Fluid Dynamics

CTCR Coolant Thermal Capacity Rate

DB Data Base

Eff Effectiveness

FOB Objective Function

FV Finite Volume

GT Gas Turbine

UJ Heat Transfer Coefficient of j-th flow

HDGT Heavy Duty Gas Turbine

HGTCR Hot Gas Thermal Capacity Rate

IGCC Integrated Gasification Combined Cycle

LHV Low Heating Value

LP Lumped Performance

m Mass Flow

n Shaft Rotational Speed rpm

N Index

NTU Number of Heat Transfer Units

p Pressure

P Power

PR Pressure Ratio

RH Relative Humidity

Q Heat

s Thickness

S Surface

SoA State of the Art

T Temperature

Tc Coolant temperature

Tf Firing Temperature

Tg Hot gas temperature

Tw Blade wall temperature

TBC Thermal Barrier Coating

TIT Turbine Inlet Temperature

TCR Thermal Capacity Ratio

U Global Heat Transfer Coefficient

UEBC Uncooled Equivalent Brayton Cycle

VIGV Variable Inlet Guide Vanes

Page 7 of 45

Greek Symbols

Pressure Ratio

Thermal Conductivity

c Thermal Capacity Ratio

Heat Transfer Effectiveness

c Cooling Effectiveness

Density

Subscripts

0 Reference Condition / Standard Condition

b Blade

bJ j-th bleed

c Coolant

C Compressor

E Expander

ex Exhaust Gas

g Gas

i Inlet

N Nominal

o Outlet

RJ j-th rotor

SJ j-th stator

Page 8 of 45

1 Introduction

Modern Heavy Duty and Aero Gas Turbine engines are the most complex system being

operated because many interconnected phenomena assure the maximum exploitation on the

sophisticated high performance material based devices (e.g. vanes, blades, shrouds, seals, etc.)

for a sufficient operation time at temperatures that assure economic revenue of the money

investments.

Gas Turbine engine performance work (work for kg of the air entering the compressor –

power for kg/s of the air entering the compressor) and efficiency (i.e. heat consumption for an

unit of produced work, heat rate for an unit or delivered power) depend on the flow-weighted

mean temperature of the working fluid entering the expander (TIT), on the exhaust

temperature that is related to the TIT, on the pressure ratio of the expander, on the fuel

composition and of its low heating value , on the entropy production (or dissipated work), on

the boundary conditions (ambient, speed, etc.) and on the heat removed from the expander

along the flow path.

Of course temperature levels are related to the component life consumption rate due to

operation that involves also stress, corrosion, erosion and other facts that are summarized

under the creep concept.

To rise firing temperatures maintaining the temperatures of the GT hot components lower

than the threshold allowed by the material characteristic the cooling concept has been

adopted. This means that some fresh cooling mean is introduced inside the expander disks,

blades, etc. to remove the heat flowing from the outer main stream and to overall decrease the

metal temperature. Under this context internal channels with enhancer heat transfer devices

lead the coolant mass flow to imping some areas of the internal surface and escape to the

lateral surface especially at the leading edge producing a film and at the trailing edge passing

through slots made of finned surface.

In the H2-IGCC Project context RO3 has developed an Generic 300MW F Class Gas Turbine

Simulator that adopts a Lumped Performance (LP) methodology employing a Finite Volume

(FV) approach based on detailed Architecture, Geometry, Lumped Physics and Chemistry

including all the empirically known phenomena characterizing the specific Gas Turbine

behaviour. Such a simulator has been built up taking the Best Available Technologies (BAT)

connected to the existing F, G and H Class Gas Turbines of many Manufacturers into account.

Features of such a simulator have been developed as to be close to those of the existing

machines of some European O&M’s.

The main quantities characterizing the GT (Firing Temperature, Turbine Inlet Temperature,

Turbine Exhaust Temperature, Exhaust Mass Flow, Pressure Ratio, Power, Overall

Efficiency, etc.) has been taken during the Generic 300MW F Class GT Simulator

development into consideration, looking at the BAT and to the selected architecture of the

Page 9 of 45

Generic 300MW F Class GT that has been chosen to that of the Ansaldo AE 94.3A and

Siemens SGT5-4000F ones, the manufacturer being partners of the project.

In this deliverable, the preliminary evaluation of the overall cooling mass flow is discussed.

To perform this calculation after a preliminary cycle calculation, in which GT global

quantities such as temperatures, mass flows, etc. have been evaluated, the overall coolant

mass flow has been established by the adoption of global models according to the BAT State

of the Art (SoA) and Technological Background.

Once the overall coolant mass flow has been evaluated, cooling requirement for each

expander row has been calculated taking the RO3 lumped model approach into account.

Coolant mass flows required to cool the Generic 300MW F Class Gas Turbine fed by

Methane at the nominal running point are reported. Such a calculation has been also

performed for the 33 MJ/kg Syngas fed re-staggered Gas Turbine that is the pervious one with

the 1st Nozzle Vane (NV) opened (re-staggered) to accommodate the increase of the turbine

inlet mass flow connected with the reduction of the LHV.

Page 10 of 45

2 Uncooled Cycle Calculation

A preliminary evaluation of a methane (CH4) fed GT cycle has been performed to evaluate

the relevant quantities (temperature, pressure, etc.) in the GT main stations (compressor inlet

and outlet, expander inlet and outlet, etc.) that allow to establish global parameters need to

develop the Generic 300MW F Class GT Simulator, according to the present SoA.

In figure 1, the ideal (12s3’4’s 1), the real (123’4’1) and the Uncooled Equivalent (12341)

Brayton Cycles are represented:

Fig. 1: Scheme of a GT Brayton Cycle – Not to Scale

The Uncooled Equivalent Brayton Cycle model developed by RO3 takes the various GT

losses by the introduction of polytropic efficiencies (compressor, expander) as well as the

combustion efficiency and by the introduction of the total pressure loss both in the

combustion chamber and in the exhaust duct into consideration. Under this assumption the

ideal cycle (12s3’4’s 1) is stretched in the UEBC (12341). Schematically, the sketch of the GT

well representing the UEBC is depicted in figure 2:

Fig. 2: Scheme of a Generic 300MW F Class GT

Page 11 of 45

UEBC Calculation has been performed taking data of the present State of the art of the BAT

GT. In table 1 some of these data are given:

Table 1: HD GTs Characteristic Quantities

Power

[MW]

Efficiency

[%]

Exhaust Temp

[°C]

Exhaust Mass

[kg/s]

Pressure Ratio

[#]

Siemens (2008)

SGT5 - 4000F 292 39.8 577 692 18.2

Siemens (2013)

SGT5 - 4000F 295 40.0 586 692 18.8

Ansaldo

AE 94.3A 294 39.7 580 702 18.2

Mitsubishi (2012)

M701F4 324 39.9 592 730 18

Alstom (2012)

GT 26* 326 40.3 603 692 35

*: HDGT with a ‘Sequential Combustion’

To perform the calculation, some parameters have been fixed to be varied into a feasible

domain according with the BAT to evaluate the relevant quantities of the GT Cycle.

o ηc: compressor efficiency

o ηe: expander efficiency

o ηb: combustion efficiency (taking the unburned into account).

The combustion efficiency does not take the not fully adiabaticity of the

process into account. This aspect is considered instead when the

combustor efficiency is introduced.

o Qsb: GT radiation and convection heat losses (some 1%)

o ∆p: pressure loss (combustor and exhaust duct)

o P loss: Losses (mechanic loss and electric loss)

All the mechanic loss (including the thrust) are schematically lumped in

the section A of the figure 2. Electric loss includes both the transformer

loss and the electric generator loss.

By the solution of a set of equations fully describing the Uncooled Equivalent Brayton Cycle,

properly bounded by a set of inequalities, the quantities needed for the preliminary cooling

calculation have been evaluated.

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Inlet quantities and outlet quantities of the UEBC Calculation are given in tables 2 and 3:

Table 2: Input Data for Cycle Calculation

AE 94.3A SGT5-4000F

BOUNDARY CONDITIONS (b)

p1 [kPa] 101.3 101.3

T1 [°C] 15.0 15.0

[xx]1 [#]m dry air + RH60%

DATA (d)

[xx]f [#]m pure methane

LHV [kJ/kg] 50060 50060

P* [MW] 294 292

ηGT* [#] 0.397 0.397

mex* [kg/s] 702 692

Tex* [°C] 580 577

* [#] 18.2 18.2

∆pcc/p2 [#] 0.05 0.05

∆pe/p1 [#] 0.03 0.03

ηm [#] 0.998 0.998

ηge [#] 0.968 0.968

Table 3: Cycle Calculated Quantities

AE 94.3A SGT5 - 4000F

COMPRESSOR

T1 [°C] 15 15

T2 [°C] 409 409

p2 [kPa] 1844.1 1844.1

etapc [#] 0.929 0.928

LC [kJ/kg] 411 411

COMBUSTION CHAMBER

etacc [#] 0.99 0.99

AFR [#] 46 46

EXPANDER

T3 [°C] 1246 1246

p3 [kPa] 1751.9 1751.9

etape [#] 0.866 0.871

LE [kJ/kg] 854 858

GAS TURBINE

LTg [kJ/kg] 428 431

Page 13 of 45

Taking data of the Reference GT given in table 1 (i.e. exhaust mass flow) into account the

compressor inlet mass flow and fuel mass can be established as well as power that have not

been calculated by the Uncooled Equivalent Brayton Cycle calculation because it is a specific

cycle calculation.

Table 4: Cycle Mass Flows

AE 94.3A SGT5 - 4000F

Mass Flow

mCi [kg/s] 687.2 677.3

mf [kg/s] 14.8 14.7

mex [kg/s] 702.0 1844.1

As a result of the UEBC evaluation , the expander inlet temperature T3 has been established.

According with figures 1 and 2, in the UEBC the T3 is the Turbine Inlet Temperature (TIT)

defined by the ISO 2314,where Turbine Inlet Temperature is defined:

‘defined arbitrarily as a theoretical flow-weighted mean temperature before the first-stage stationary blades

calculated from an overall heat balance of the combustion chamber with the gas mass flow from combustion

mixed with the turbine cooling air mass flows prior to entering the first stage stationary blades’.

Accordingly, TIT can be approximated by the rule (1) according to figure 3:

g pg g cj pj cj

j

mix pmix

m c T m c T

TITm c

(1)

mixm being the sum of the various coolant flows cjm and of the gas mass flow

gm and pmixc

being the pressure constant specific heat of the mixture depending on many parameters.

0 0[ ( , ), ( , )]pmix pg pcjc f c TIT T c TIT T

TIT is a relevant temperature because it relates the overall coolant mass flow to the inlet hot

gas mass flow entering the gas expander and the coolant temperatures to the firing

temperature.

Fig. 3: Turbine Inlet Temperature Nomenclature

Page 14 of 45

3 GT Global Model for the evaluation of the overall cooling mass flow

Taking results of the uncooled equivalent Brayton cycle calculation as well as the

technological level (Class) of the Gas Turbine into consideration, the overall coolant mass

flow required to perform the cooling purposes can be evaluated by the adoption of global

models. Such models relate the overall coolant mass flow to some relevant temperatures

(compressor outlet temperature, metal temperature, firing temperature that is strictly related to

the TIT), to the compressor inlet or expander inlet mass flow, to the main flow and coolant

flow properties and to some parameters that well represent the Class of the Gas Turbine

(introduction of some coefficients).

The overall coolant flow can be express as a function of such parameters:

1 2( , , , , , , , ,...)g pg pc b f cexmc f m c c T T T k k

For the preliminary evaluation of the overall coolant mass flow, the coolant temperature Tc

has been assumed in the range of some 400-500 °C and the blade temperature Tb in the range

of 830-895 °C. Such temperatures are defined arbitrarily as reference lumped temperatures of

the RO3 GT global model. In table 5, evaluation of the overall coolant mass flow for the

extreme values of the coolant temperature and blade temperature is reported:

Table 5: Evaluation of the overall coolant mass flow

for various coolant and blade temperature, respectively

By the assumption of some coefficients taken for the SoA, the overall coolant mass flow has

been calculated and by averaging these results, an overall value is of some 26% of the

compressor inlet mass flow:

26%cj

j

m of inlet compressor mass flow

mc 165 kg/s

cpc 1.1 kJ/(kgK)

mg 523 kg/s

cpg 1.3 kJ/(kgK) mci 685 kg/s

Tcexit 400 °C mc/mci 24.1 %

Tf 1440 °C

Tb 830 °C

k1 0.1884 #

k2 1 #

mc 215 kg/s

cpc 1.1 kJ/(kgK)

mg 523 kg/s

cpg 1.3 kJ/(kgK) mci 685 kg/s

Tcexit 500 °C mc/mci 31.4 %

Tf 1440 °C

Tb 830 °C

k1 0.1884 #

k2 1 #

mc 129 kg/s

cpc 1.1 kJ/(kgK)

mg 526 kg/s

cpg 1.3 kJ/(kgK) mci 685 kg/s

Tcexit 400 °C mc/mci 18.8 %

Tf 1440 °C

Tb 895 °C

k1 0.1884 #

k2 1 #

mc 162 kg/s

cpc 1.1 kJ/(kgK)

mg 526 kg/s

cpg 1.3 kJ/(kgK) mci 685 kg/s

Tcexit 500 °C mc/mci 23.6 %

Tf 1440 °C

Tb 895 °C

k1 0.1884 #

k2 1 #

Page 15 of 45

Evaluation of the overall coolant mass flow given by the RO3 model leads to a value of that

mass flow that agrees with the coolant ratio (mcool/mcompr) founded in the technical

background. Accordingly, in the present State of the Art models similar to that of RO3

research group has been found and evaluation of the overall coolant flow gives result not far

from the RO3 calculated.

In the paper [13] a similar approach of that presented by RO3 has been found. Coolant mass

flow is evaluated, according to the GT sketch given in figure 4, as a function of relevant

temperature, properly coefficients and mass flows:

Fig. 4: Sketch of the GT presented in the paper [13]

The paper states:

The parameters b and K were adjusted to yield a net efficiency of 38.50 % at a combustor exit temperature of

1425 °C with a cooling fraction of 22 %. … The cooling fraction is the cooling fluid mass flow rate divided by

the compressor inlet mass flow rate…

Page 16 of 45

Values similar to that established by RO3 have been found in other papers:

Moreover, in the paper of Ashok Rao., 2010, ‘1.3.2 Advanced Bryton Cycles’ the overall

coolant mass flow is related to some relevant quantities:

The paper states:

In a state-of-the-art air-cooled gas turbine with firing temperature close to 1320ºC (2400ºF), as much as 25% of

the compressor air may be used for turbine cooling, which results in a large

parasitic load of air compression. In air-cooled gas turbines, as the firing temperature is increased, the demand

for cooling air is further increased. …

Page 17 of 45

4 Heat transfer scheme and cooling scheme

Various heat transfer phenomena have to be taken during the design of the cooling system

into consideration. Under the effect of convection, radiation and conduction the heat of the

main stream (the hottest one) flows through the various GT components, each of them

characterized by a thermal gradient. Accordingly, lot of the Gas Turbine components (disk,

shroud, sidewall, blade, cavity, etc.) need to be cooled by some ‘cold’ air to maintain their

temperature under a defined threshold value. Some coolant flows are required to achieved this

purpose. Moreover, coolant flows are used for services (sealing, balance, etc.). Thus, coolant

flows are not solely used for blade surface cooling, but for all the aspects concerning the GT

cooling. Figure 5 represents schematically the cooling flows along a Generic 300MW F Class

Gas Turbine:

Fig. 5: Cross Section of the Cooling Paths (SIEMENS)

Moving from the 1st vane of the compressor to the last rotor row of the gas expander, the main

flow path is split in various stations for various purposes, as schematically represented in fig.

5. Some fractions of the compressor inlet mass flow are extracted at different compressor

stages and move to the expander stages mixing with the hot gas main flow. Main flow at the

compressor exit is split in various fraction. One is directed to the 1st Nozzle Row, a second

one is addressed to the 1st Rotor Row while the major of them is used for the combustion

process. All the fluxes are also adopted to cool the combustion chamber externally and

internally, respectively. Indeed, Combustor is also taken in the complex cooling path into

consideration because of the high temperature of the combustion process. Liners of the

Annular Combustor are cooled inside where the flame or combustion occurs. The inner of the

liner is cooled by film and also the Liner Metal Temperature (LMT) is reduced by the

interposition of the Thermal Barrier. The outer of the combustor is protected by the coolant

Page 18 of 45

flows directed to the 1st expander stage. The extracted mass flows, both from the compressor

stages both at the combustor inlet, are not used for the 100% to the surface blade cooling but

also for other features.

As an example of the high complexity of the heat transfer phenomena occurring in the Gas

Turbine, in figure 6 a sketch of the heat fluxes moving from the combustion chamber to the

casing and to the shaft is given:

Fig. 6: Schematic View of the main stream and coolant streams along the combustor

and of the heat fluxes moving through the GT to the casing and to the inner components (shaft, disk, etc.)

Convection, radiation (especially for the combustion chamber) and conduction phenomena

have to be taken for the GT cooling into account. Indeed, high temperatures are reached

during the combustion process so systems to maintain the component temperature under a

threshold upper limit are usually adopted. Both the coolant flow addressed to the expander

and the main flow sent to the burner lap the outer surface of the liner, while the inner of the

liner is cooled by film and also the Liner Metal Temperature (LMT) is reduced by the

interposition of the Thermal Barrier. Even if the complex system of the combustion chamber

is cooled, some heat fluxes flow through the metal to the casing and to the shaft, respectively.

Taking the outer (casing) and the inner (disks, shaft, etc.) components of the machine into

account, main flows and coolant flow are subjected to convection and radiation heat transfer

phenomena. According to figure 6, these streams increase their temperatures moving along

the combustor.

Page 19 of 45

4.1 Flow in the Expander Stages

Description of the purposes that the coolant flows has to perform allows to better understand

which peculiarities of the GT cooling are taken by the RO3 Lumped Model into account.

According to figure 5, the ‘cooling channels’ of the compressor rotor rows extractions are

highlighted by the red circle. This channels lead the coolant flows to the respectively

expander stages in order to cool all the components thermally stressed.

List of the main row components that required to be cooled to maintain their temperatures

under the threshold value is given and by the help of some exemplificative pictures the

expander flow paths are described.

Disk

Disk Cavity

Shroud

Platform

Shank

Sidewall

Airfoil Surface

Tip Cap

others

Moreover coolant flows are used for the services. Such a services are as an example the piston

balance, the sealing and other as shown in figure 7 below:

Fig. 7: Schematic view of the cooling paths along the disks – As example

Coolant mass flows extracted from the compressor stages have different paths and are

addressed both for stator row and for the rotor row. By the simplified adoption of Fig. 8, is

possible to better understand which are the various coolant flow paths along the gas turbine.

Page 20 of 45

Fig. 8: Example of a Generic Gas Turbine Cooling Path along Stator and Rotor Row

The path from the extraction (bleeding) sections to the respectively expander rotor row is the

cooling passage represented by L in Fig. 8.

The coolant flows pass through the shaft before entering the disk cavity and the disk.

Bleed extractions addressed to the stator (nozzle) rows pass externally (around) the machine

lapping the case before re-entering in the respectively row.

The coolant flow addressed to a Stator Row assuming the schematization of Fig. 8 is used for

various purposes:

Cooling of the Airfoil Surface (inner and outer) - D in the Fig. 8

Cooling of the Platform and Sidewall (inner and outer) - E in the Fig. 8

Mixing with the main stream, downstream the Stator Vane - G in the Fig. 8

Extracted mass flow for the Stator Row cooling is used for various cooling surfaces. For this

reason the overall extracted mass flow is split in various fractions, adopted for the various

cooling purposes, respectively. A schematic view of the Stator Row cooled components is

given in Fig. 9:

L

D

E

E

G

B

A

C

A

F

H H

Page 21 of 45

Fig. 9: Schematic View of the Cooled components of the Stator Row – As Example

As for the Stator Row also for the Rotor Row, coolant flows are used for various row

components cooling and the overall mass flows (extracted from the compressor) are divided

into minor flows for different purposes:

Cooling of the disk outer – H in the Fig. 9

Cooling of the Airfoil Surface (inner and outer) - B in the Fig. 9

Cooling of the Shank - C of Fig. 9

Sealing - F in the Fig. 9

Mixing with the main stream, downstream the Rotor Blade – A in the Fig. 9

From the Rotor Blades, heat fluxes move to the shaft passing through the various components.

A typical temperature distribution along the disk is given in Fig. 10:

Fig. 10: Typical Temperature Distribution along a 1st Stage Aeronautic Rotor Disk – As Example

Page 22 of 45

All these aspects (components cooling, services, sealing, etc.) have to be considered to

evaluate the coolant mass flows and the various temperatures of the phenomena. Indeed, heat

removed from all the hot components (disk, shank, etc.) flows towards the fractions of the

overall coolant flow designed to perform the defined purpose (cooling, service, sealing, etc.).

To ensure that all the temperature of the various components are sufficiently lower than the

threshold value, the bled mass flow is split in various fluxes. A first assumption for all the

Stator Rows, except for the first one, is that a 60% of the overall coolant flow is addressed to

the blade surface cooling and the other 40% is used for the sidewall, platform and for all the

other components previously described. In Fig. 11 a detailed figure of the Stator (Nozzle)

Row cooling components is given:

Fig. 11: Schematic View of a 1st Nozzle Vane Cooling Components – As Example

Coolant mass flows distribution for the Rotor Rows is pretty similar to the Stator Row. Some

65% of the overall extracted coolant flow is used for the blade surface cooling and the rest

some 35% is addressed to the other row components (dovetail serration, shank, platform,

etc.). In Fig. 12 a detailed representation of a Rotor Blade cooling components is given:

Fig. 12: Schematic View of a 1st Rotor Blade Cooling Components – As Example

Page 23 of 45

Of course even if the stator row and the rotor row blades of the last expander stage are

uncooled (not cooled by internal coolant flows and not film cooled). Some coolant flows are

addressed anyway to that stage because the disks have always to be cooled. Thus a heat flux

from the hot parts to the cold one exists. In figure 13, a schematically comparison of the

various coolant flows between the cooled blade and uncooled blade is sketched. Moreover,

the RO3 GT cooling model is schematically represented in figure 14.

Fig. 13: Comparison between cooled blade and uncooled blade coolant flow

Each Heat transfer process is characterized by a ‘heat transfer effectiveness’ if a

Effectiveness - Number of Transfer Unit (ɛ-NTU) approach is adopted to model the GT

cooling system. Taking the various heat transfer phenomena characterized by a certain

effectiveness into account, the coolant flow fraction distributions has been evaluated

according to the above:

Table 6: Fractions of the overall mass flow for each row (in percentage %)

STAGE

ROW 1S 1R 2S 2R 3S 3R 4S 4R

Airfoil Surface 50 65 60 65 60 65 0 0

Other Purposes

(endwall, shroud,

sealing, etc)

30 35 40 35 40 35 100 100

Jet Cooling 20 0 0 0 0 0 0 0

Coolant Mass Flow Percentage % for the various purposes

1st Stage 2nd Stage 3rd Stage 4th Stage

Page 24 of 45

Fig. 14: Schematic View of the cooling path

from the compressor bleeding station to the expander row injection station

Page 25 of 45

5 Lumped Performance Features Model

According with the Deliverable 4.2.2, RO3 modelling approach is based on a FV lumped

feature and performance discretisation of components. The approach is addressed to model

any kind of machines and apparatuses made of elementary components such as: compressor

rows, expander rows, combustion chambers, heat exchangers, pumps, etc. Real three

dimensional time dependent measured flow features are taken into account by lumping on the

FV boundary models J and 1J the distributions of quantities of interest such as pressure,

velocity, temperature, etc., by means of an averaging procedure on surface and time.

Moreover the lumping procedure is adapted for the quantities that are involved in the

component performance calculation according to the implemented modules. The lumped

features are reduced to the FV central nodes NJ .

This approach can be easily adopted for a heat transfer device. The Gas Turbine cooling

system can be seen as a complex arrangement of series and parallel heat transfer devices. Heat

transferred from a fluid to the other (the performance) is related to the lumped flow features

and to the geometric features of the various components by adapting classical heat transfer

model. The connection between component features and heat transfer model is established

according to the amount of data available by detailed simulations. As an example both shell

and tube and finned tube heat transfer device lumped scheme is given in figure 15a –b:

Fig. 15 a-b: sketch of the lumped approach for heat transfer devices

Accordingly, RO3 University Simulator takes a GT cooling lumped model into account which

implies transfer of heat from the main flow (hot gas) to the coolant flows, through various

components (blade row, disk, etc.). Moreover, some heat flows from the hottest GT

components (i.e. combustion chamber) to the colder ones (i.e. shaft, casing, etc.). Taking the

description of the cooling paths along the machine into consideration, in such a lumped model

the coolant flows consider both the airfoil blade cooling and the cooling of the other parts

(disk cavities, shrouds, endwalls (sidewall) and the action of coolant as sealant flow re-

entering into the main flow. Temperatures (coolant, blade, etc.) have the meaning of lumped

reference temperature of the complex cooling process.

Page 26 of 45

6 Blade Cooling Model

Gas Turbine Blade Cooling can be seen as a series of layers characterized by different heat

transfer phenomena. In figure 16 sketch of that schematization is depicted:

Fig. 16: Sketch of a Rotor Blade temperature distribution along the layers

Moving from the inner side (coolant) to the outer one (main stream) the following heat

transfer layers can be described:

o Internal Cooling Flow Bulk Material: convection heat transfer

Coolant mass flow entering the blade is used to remove the heat flowing from the

metal. Flow velocity, gas composition, architecture and geometry of the blade are

some parameters that influence the internal convection heat transfer phenomena.

o Bulk Material and Thermal Barrier Coating: conduction heat transfer

Both for the Bulk Material (BM) and for the Thermal Barrier Coating (TBC) the

heat flux coming from the outer surface passes through the various conductive

layers characterized by a thickness js and by a thermal conductivity j , that is a

function of the heat transfer temperatures.

o Thermal Barrier Coating Hot gas: prevalent convection heat transfer

The hot gas exiting the combustion chamber and entering the expander is at high

temperature. The model takes both the radiation effects and the convection into

account by considering the heat transfer as a prevalent convection phenomena.

By the adoption of the most suitable expression, the hot gas prevalent convection

heat transfer coefficient Ug can be evaluated:

Page 27 of 45

Re Pr

q

gm n

W

TNu A

T

(1)

Nu being the non-dimensional group of Nusselt, , Re being Reynolds number, Pr

being Prandtl number, Tg being the gas temperature, TW being the wall temperature

and A, m, b, q coefficients depending on the phenomena. By the adoption of

different value of these coefficients also internal convection heat transfer

coefficient Uc0 can be evaluated.

The various heat layers can be seen as a thermal equivalent circuit and schematically the heat

transfer phenomena previously described can be represented as a series of thermal resistance

as shown in the figure 17:

Fig. 17: Simplified view of the thermal resistance for a generic blade

To improve the performance of the blade in term of rate of life consumption is desirable to

increase the outer thermal resistance (reduce the external heat transfer coefficient), to reduce

the inner thermal resistance (increase the internal heat transfer coefficient) and to adopted a

thermal barrier coating layer characterized by an high thermal resistance (high conductivity).

Various techniques are employed both on cold side and on the hot side to better remove the

heat from the blade.

On the coolant flow side, adoption of some architectural devices as the turbulence promoter,

the rib arrangement, the pin fins and of jet impingement technique leads to increase the

internal heat transfer coefficient. Each enhancing system can be seen as a corrective

coefficient fjk greater than 1 of the equivalent smooth heat transfer coefficient Uc0.

Accordingly, in figure 18 temperature profile modification on the coolant side owing to the

enhancing system of the heat transfer coefficient is given:

jet impingement fji >1

turbulence promoter ftp >1

rib arrangement ftp >1

pin fins fpf >1

Page 28 of 45

Fig 18: Schematic view of the enhance system of the internal heat transfer coefficient

Turbulence promoter are widely employed in Heavy Duty Gas Turbine inner channels in

order to enhance the internal heat transfer coefficient. Taking ribs configuration according to

Data Base (figure 19-a) into consideration, in figure 19-b the increase of heat transfer

coefficient is shown.

Fig. 19 a-b: a) rib distribution – b) Influence of Turbulent promoter on the NU number

Page 29 of 45

Adoption of impingement concepts leads to enhance the internal heat transfer coefficient. The

overall increase of the Nusselt number depends on many architectural and geometrical

parameters taken from Data Base and from the HDGT State of the Art. Nusselt non-

dimensional group versus some architectural ratios is shown in figure 20:

Fig 20 : Influence of jet impingement architecture on internal heat transfer coefficient

Heat flux coming from the blade layers is mitigated by the coolant mass flow taken from

compressor. Internal heat transfer coefficient 0cU is evaluated taking internal diameter,

velocity, mass flow, viscosity, etc. into account. Internal devices, suitably arranged (pins, rib,

etc.) as well as the jet impingement are designed to enhance internal heat transfer coefficient.

Coolant mass flow passes through multi-pass channel, increasing the effective surface of the

heat transfer, before exiting from the blade and mixing with the main hot gas stream. The

contribution of turbulence promoters, ribs arrangement, pin fins and jet impingement are

taken into account by expressing the coolant heat transfer coefficient:

0c c Tp ji ra pfU U f f f f

On the other side, the hot one, introduction of techniques to reduce the external heat transfer

coefficient are taken into consideration. The adoption of film cooling allows to depress the

hot gas heat transfer coefficients (Ug0) by the correction of a ffilm coefficient, lower than 1,

because of the cold insulating layer between the hot gas stream and the wall of the blade.

Accordingly, film cooling can be also seen as an additional thermal resistance layer

characterized by an equivalent thickness and thermal conductivity. In figure 21, temperature

profile with and without film cooling is depicted:

Page 30 of 45

Fig 21: Schematic view of the depression of the external heat transfer coefficient owing to the film cooling

Main stream prevalent convection heat transfer coefficient 0gU is related to some parameters

such as velocity, efflux area, conductivity, viscosity, etc. External heat transfer coefficient

assumes different values for different points among the blade profile as shown in fig.22. By

the adoption of RO3 lumped model hot gas heat transfer coefficients have been evaluated for

the various blade rows. When the film cooling occurred, external heat transfer coefficient is

depressed by the coolant mass flow exiting from the blade row holes realizing a thin cold film

that protects the blade.

Fig. 22: Typical heat transfer distribution among the blade row surface

Heat transfer coefficient distribution on pressure and suction side and film cooling influence

on the phenomena are shown in figure 23:

Page 31 of 45

Fig. 23: External heat transfer coefficient depressed by the film cooling

The hot gas heat transfer coefficient can so be expressed:

0g g filmU U f

1filmf being the film cooling coefficient.

Also BM and TBC layer influences the heat transfer process. Bulk Material and Thermal

Barrier Coating thermal resistances are evaluated taking the thickness sj and the thermal

conductivity of the layer into account. Changing the thickness of the TBC layer and the

TBC material composition, the coolant mass flows required to maintain the same ratio of life

consumption change significantly. As an example, in figure 24 modification of the coolant

flows versus the TBC thickness is presented:

Fig. 24: Influence of the Thickness TBC layer on the coolant flows

Page 32 of 45

6.1 Cooling Effectiveness

Combining the various heat transfer processes (phenomena) together the overall GT blade

temperature profile is sketched in figure 24.

Fig. 25: Temperature profile along the various blade layers

From the technology point of view a global relationship exists between the characteristic

temperatures of cooling phenomena and cooling effectiveness. For each blade row the cooling

effectiveness can be expressed:

g W

c

g c

T T

T T

(2)

Such a cooling effectiveness is an empirical result and is an empirically established

relationship among architecture, geometry of the coolant system (platform, blade, shroud,

etc.) thermic and thermal barrier, bulk material as well as main stream and coolant parameter

relevant for the heat transfer process. It is a results of coupling, of a coolant stream and blade

seen as an heat transfer device and of the outer stream.

6.1.2 Effectiveness – Number of heat Transfer Unit

To establish a global relation to express cooling effectiveness c in terms of characteristic

quantities of the overall phenomena, such as coolant and hot gas mass flows, architectural and

geometric parameters as well as heat transfer coefficients, the problem can be addressed by

adopting the Effectiveness VS Number of heat Transfer Unit NTU approach.

Page 33 of 45

Effectiveness represents the effective heat Q that can be exchanged versus the heat Q that

could be hypothetically exchanged by a heat transfer device of infinite surface (3):

Q

Q

(3)

The Number of heat Transfer Unit is expressed by the relation (4):

p

U SNTU

c m

(4)

U being the heat transfer coefficient, S the characteristic Surface of phenomena, pc the

specific heat of the fluid and m the mass flow.

Depending on geometry, holes arrangement, streams directions (equicurrent, countercurrent)

and so on, the most adequate formulation that relates to NTU can be adopted, taking Data

Base and the State of the Art into consideration:

( , , ,....., , , )g c gf m m U NTU geometry architecture (5)

According to nomenclature of figure 25 cooling effectiveness c can be evaluated as a

combination of effectiveness related to elementary heat transfer processes taking film cooling,

impingement, conduction and all aspects into consideration. Moreover, evaluation procedure

of cooling effectiveness c has been performed taking relationship of counter current heat

exchange from Data Base into account. Accordingly, the following heat transfer process have

been described:

Hot gas – Thermal Barrier effectiveness

1

1 1g NTU

g TB

Te

T T

(6)

1

1

g

g pg

U SNTU

m c

(7)

0g g FilmU U f (8)

gU being the heat transfer coefficient of the hot stream corrected by film cooling

coefficient (if film cooling is adopted) depressing the hot gas heat transfer coefficient

0gU . Filmf is lower than 1.0.

Page 34 of 45

In the various gas expander row, hot gas stream reduces its temperature both because

of the expansion (uncooled) and because of the injection of the coolant flows into the

main stream. The latter aspect lead to a temperature differencegT strictly connected

to the heat transfer process. A schematic equivalent representation, not to scale, of the

cooling effect on the gas side is given in figure 26:

Fig. 26: schematically main stream temperature decrease – Not to scale

Hot Gas – Bulk Material

2

2 1g NTU

g W

Te

T T

(9)

2

2

g

g pg

U SNTU

m c

(10)

2

1

1 TB

g TB

Us

U

(11)

2U being the heat transfer coefficient taking convection of the main stream and conduction of

the TB layer into consideration.

Page 35 of 45

Hot Gas – Coolant

In this case two different fluids take part at the heat transfer phenomena. According to

Data Base, expression of effectiveness is different from the (6) and (9) because Thermal

Capacity Ratio TCR must be considered (12):

c pc

g pg

m c

m c

(12)

Coolant stream is the lower heat thermal capacity fluid that must be put at the dominator

of NTU expression:

3

3

(1 )

3 (1 )

1

1

NTU

Co Ci

NTU

g Ci

T T e

T T e

(13)

33

i

c pc

U SNTU

m c

(14)

3

1

1 1 1c cTB

g g TB g BM c

US Ss

U S S U U

(15)

0c C TP IU U f f being the internal coolant heat transfer coefficient corrected by enhancing

coefficient related to turbulence promoter and impingement effect, respectively.

BMU being the heat transfer coefficient of the bulk material, TB

TB

s being the heat transfer

coefficient trough the thermal barrier.

In this simple application, expressing cooling effectiveness as (16):

g W

c

g c

T T

T T

(16)

and combining effectiveness of sub-process (9) and (13):

3

2 ( )

g W

g c c co

T T Tg

T T T T

(17)

Substituting (17) into (16), cooling effectiveness is expressed in terms of mass flows,

architectural and geometrical parameters (19) taking conservation of energy into account (18):

( )c pc c co g pg gm c T T m c T (18)

3

2

c pc

c

g pg

m c

m c

(19)

Page 36 of 45

Finally combining (19) with (9), (12) and (13) analytic expression, for a really simple case, of

cooling effectiveness c is obtained and given as rule (20):

3

3

2

(1 )

(1 )

1

1

1

NTU

NTU

c NTU

e

e

e

(20)

Such an effectiveness depends on many parameters and empirically known aspects:

( , , , , , , , , , , ....)c g pg c pc i o j jf m c m c U U s architecture geomtry etc

Accordingly, RO3 GT Cooling model based on lumped performance features includes all the

aspects previously described (airfoil, platform, sidewall cooling and others). The best fit

relation to establish the cooling effectiveness (taking architecture, technology, flow feature,

etc. into account) can be described by the following equation:

2

1

k

cj k e (21)

k1 and k2 being coefficients taking cooling modern technologies into account.

By the adoption of this expression of the Cooling Design curves, the coolant flow for each

stator row and rotor row, respectively, can be established. In figure 27, such RO3 curves for a

generic stator row and a rotor row are given:

Fig. 27: RO3 Cooling Design Curve – Stator Row and Rotor Row

Page 37 of 45

The curves allow to relate the cooling effectiveness to the thermal capacity ratio (or a similar

quantity accounting the coolant stream).

Each curve is characteristic of a certain level of technology.

o type of cooling techniques (film cooling, transpiration, impingement, etc.)

o material properties

o blade architecture

o kind of coolant (steam, air, etc.)

o etc…

Curves similar to that of RO3 relating cooling effectiveness to thermal capacity ratio are

represented in figure 28, in which the various cooling techniques represent a different curve.

Fig. 28: Cooling Effectiveness versus Thermal Capacity Ratio

In the State of the Art of GT cooling, expression (curves) similar to that of the RO3 lumped

model, relating cooling effectiveness to the coolant flows has been matched.

In figure 29, Gross Cooling Effectiveness Curves (Cooling Effectiveness defined in RO3

Model) versus heat loading parameter (accounting for coolant flow) are plotted for the various

cooling techniques. In figures 30 and 31, cooling effectiveness versus coolant/gas heat flux

ratio and TCR ratio are given respectively. Accordingly, trends of that curves are close to

RO3 ones.

Page 38 of 45

Fig. 29: SoA – Gross Cooling Effectiveness VS Heat Loading Parameter

Fig. 30: SoA –Cooling Effectiveness VS Coolant/Gas Heat capacity flux ratio

Fig. 31: SoA –Cooling Effectiveness VS TCR

Page 39 of 45

7 Design Point Result

According with the lumped approach described in the paragraph 5, in RO3 University

Simulator lumped cooling model the temperatures have the significant of the overall ‘cooling

row phenomena’, thus the coolant temperature TC is not the injection temperature but the

lumped reference temperature. Moreover, the coolant mass flows have the significant of the

overall flow required to cool airfoil surface, disk, sealing and all the other aspects previously

described.

Evaluation of coolant mass flows and of the blade wall temperature of the Lumped Model,

has been performed both for the Methane fed GT and for the 33MJ/kg Syngas fed GT, being

the previous one with the 1st Nozzle Vane re-staggered (opened) to maintain the same

pressure ratio:

Fig. 32: 1st Nozzle Vane re-staggering – As Example

Input data for the Methane GT are given in tables 7:

Table 7: Sizing Data – Methane

Gas Expander Sizing

Fuel [#] CH4

LHV [MJ/kg] 50

VIGV [%] 100.0

n [rpm] 3000

pamb [kPa] 101.3

Tamb [°C] 15

RH [%] 60.0

mCi [kg/s] 685

β [#] 18.2

TC [°C] 500

mEi [kg/s] 523

pex [kPa] 104.3

In tables 8, results of Lumped Model properly adapted to the H2-IGCC context are given for

Methane Fuel (50MJ/kg) fed GT

Page 40 of 45

Table 8: Results of the Lumped Model for cooling requirement (Methane)

Stage Row mc [kg/s] Tb [°C]

1 s1 ms1 44 Tbs1 895

r1 mr1 40 Tbr1 880

2 s2 ms2 30 Tbs2 820

r2 mr2 23 Tbr2 810

3 s3 ms3 12 Tbs3 790

r3 mr3 15 Tbr3 760

4 s4 ms4 6 Tbs4 724

r4 mr4 7 Tbr4 613

Input data of the sizing procedure of the cooling system are given in table 9. Results of

Lumped Model properly adapted to the H2-IGCC context are given for Syngas Fuel

(33MJ/kg) fed GT are presented in table 10:

Table 9: Sizing Data – 33MJ/kg Syngas

Input Data

Fuel [#] Syngas

LHV [MJ/kg] 33

VIGV [%] 100

n [rpm] 3000

pamb [kPa] 101.3

Tamb [°C] 15

RH [%] 60.0

mCi [kg/s] 685

β [#] 18.2

Tc [°C] 500.0

mEi [kg/s] 521

pex [kPa] 104.3

Table 10: Results of the Lumped Model for cooling requirement (33MJ/kg Syngas)

Stage Raw mc [kg/s] Tb [°C]

1 s1 ms1 45 Ts1 895

r1 mr1 43 Tr1 878

2 s2 ms2 31 Tbs2 821

r2 mr2 24 Tbr2 806

3 s3 ms3 13 Tbs3 786

r3 mr3 17 Tbr3 756

4 s4 ms4 6 Tbs4 726

r4 mr4 7 Tbr4 614

Page 41 of 45

8 Off – Design

During the Gas Turbine Operations, conditions different from the design one occur.

Degradation phenomena (fouling, corrosion, erosion, etc.) influence pressure loss, heat

transfer coefficients and other aspect of the high complex system of the GT cooling.

Moreover, also during GT part-load behavior the various mass flows (compressor inlet, fuel,

extracted flows, etc.) change owing to the different pressure differences along the machine in

respect of that of the nominal point. Both the first and the second aspect are influencing

continuously the GT cooling. To account these aspects, off-design curves that relate the

cooling effectiveness to the Thermal Capacity Ratio have been developed.

For each Stator Vane and Rotor Blade a relation is able to describe the off-design behavior of

the cooling system.

2

1( )k

c k e

c pc

g pg

m c

m c

being the Thermal Capacity Ratio TCR.

Variation on the TCR and on the capability of the system to transfer heat from the hot stream

to the coolant one influences both film cooling and impingement cooling techniques. These

aspects are embedded into the model by the introduction of properly coefficients (k1, k2). The

coefficient k1 is strictly related to the Thermal Capacity Ratio because also when TCR=0

(mc=0) some heat flows from the blade to the disks and to the casing. For this reason even if

the TCR=0 the effectiveness is a little bit higher than 0.

RO3 off-design cooling model fits well with other found in the State of the Art. As an

example, in figure 33 a comparison between RO3 and Kim-Ro model is presented. In relation

to the TCR, the cooling effectiveness and the wall temperature for a reference blade are

plotted:

Fig. 33: Comparison between RO3 and Kim-Ro off design model

Page 42 of 45

For each Stator Vane and Rotor Blade the properly cooling off-design curve has been derived

taking the design (nominal) point described by an effectiveness and TCR of each row into

account. In figure 35, off-design curves for each row of the 4 stage Generic 300 MW F Class

GT are depicted. According to the RO3 GT cooling lumped model that considers the various

heat transfer processes, off-design curves have been presented also for the uncooled stages

(blade not internally cooled by the coolant flows) in which anyway some heat is conducted by

the blade to the disk and also drained to the other components. This heat should be removed

to maintain the hot components temperature under the maximum allowable temperature. In

figure 34 a sketch of a uncooled blade is depicted.

Fig. 34: Uncooled Blade Row Scheme – As Example

Fig. 35: Off-Design cooling effectiveness VS TCR

Reference

[1] Ainely D. G., Internal Air-Cooling for Turbine Blades – A General Design Survey,

Minestry of Supply, Aeronautical Research Council Reports and Memoranda, London 1957

[2] Albeirutty M. H, Alghamdi A. S., Najjar Y. S., “Heat transfer analysis for a multistage gas

turbine using different blade-cooling schemes, ELSEVIER Applied Thermal Engineering 24

(2004), 563-577

[3] Boyce M.P., Gas Turbine Engineering Handbook 2nd

edition, Gulf Publishing Company,

2002

[4] Carcasci C., Facchini B., A numerical procedure to design internal cooling of a gas turbine

stator blades, ELSEVIER Revue Générale de Thermique 35 (1996), 257-268

[5] Cerri, G., Marra, C., Sorrenti, A., Spinosa, S., 1990a, “Iniezione di vapore nelle turbine a

gas e raffreddamento delle palette: considerazioni teoriche,” IV Convegno Nazionale Gruppi

Combinati Prospettive Tecniche ed Economiche, Florence, Italy, May 31

[6] Cerri, G., Marra, C., Sorrenti, A., Spinosa, S., 1990b, “Iniezione di vapore nelle turbine a

gas e raffreddamento delle palette: analisi di un’applicazione,” IV Convegno Nazionale

Gruppi Combinati Prospettive Tecniche ed Economiche, Florence, Italy, May 31

[7] Cohen H., Rogers G.F.C., Saravanamuttoo H.I.H., Gas Turbine Theroy 3rd

edition,

Longman Scientific & Technical, 1987

[8] Facchini B., Ferrara G., Innocenti L., ELSEVIER International Journal of Thermal

Science 39 (2000), 74-84

[9] Han J.C., Dutta S., Ekkad S.V., Gas Turbine Heat Transfer and Cooling Technologiy,

Taylor and Franis, 2000

[10] Logan E., Roy R., Handbook of Turbomachinery 2nd

edition Revised and Expanded,

Marcel Dekker, 2003

[11] Sanjay, Singh O., Prasad B.N., Comparative performance analysis of cogeneration gas

turbine cycle for different blade cooling means, ELSEVIER International Journal of Thermal

Science 48 (2009), 1432-1440.

[12] Sanjay K., Singh O., Thermodynamic Evaluation of different gas turbine blade cooling

techniques, Thermal Issues in Emerging Technologies, ThETA 2, Cairo, Egypet, Dec 17-20th

2008

Page 45 of 45

[13] Jonsson M., Bolland O., Bucker D., Rost M. (Siemens), 2005, ‘Gas Turbine Cooling

Model for Evaluation of Novel Cycles’. Proceedings of ECOS 2005, Trondheim, Norway,

June 20-22, 2005